Modified Liu-Type Estimator Based on (r − k) Class Estimator

Abstract

In this article, we introduced a new Liu-type estimator which includes the ordinary least squares estimator (OLS), ordinary ridge regression estimator (ORR), Liu estimator (LE), (k − d) class estimator, principal components regression (PCR) estimator, (r − d) class estimator, and (r − k) class estimator. Under some conditions, the performance of the proposed estimator is superior to the other estimators by using the scalar mean squares error criterion. A simulation study has been conducted to compare the performance of the estimators. Finally, a numerical example has been analyzed to illustrate the theoretical results of the article.

Keywords:

• (r − d) class estimator
• (r − k) class estimator
• (k − d) class estimator
• Liu estimator
• Mean squares error
• Multicollinearity
• Ordinary least squares estimator
• Ordinary ridge regression estimator

Mathematics Subject Classification:

• 62J12
• 62J05
• 62J07

Acknowledgments

The authors are thankful to the referees for their valuable and constructive comments which certainly improved the presentation and quality of the article. This article was completed while the second author was on sabbatical leave (2010–2011). He is grateful to the Florida International University for awarded him the sabbatical leave, which gives him excellent research facilities.